Newman and Tuck 



(FS) 



'(1) = 



j = i 



E Pj ^i . (3.28) 



j = i 



where the pressure transfer functions pj = pj(x,aj) are given by 



/ . B \ ( F s ) " 



(3.29) 



Pj = -p(-ia.+ U^j f. , j.2,3,...,6, 



and where the f j are those of Eq. (3.15). 



Forces and Moments 



The forces and moments now follow directly by integrations over the hull 

 from the formulas 



iFi + jFj + kFg = - jfpndS 



rr (3.30) 



iF4 + 2F5 + kFg = -JJprxndS. 



The splitting up of the pressure p into a wall and a free surface part leads to 

 a similar splitting of the forces, viz., 



( WALL) ( FS) /„ r,*\ 



Fi = Fi + F. (3.31) 



for all i = 1, ... 6. But since P( j)"* is a function of x (and time) only, the re- 

 sults of Appendix I, Eqs. (A1.3) and (A1.4), may be used to show that 



p(FS) 



|dxS'(x) pj^'^(x,t) 



( FS) 



f' ' = 



( FS) f . ( FS) 



F; = J dxB(x) pJj/Cx.t) 



(3.32) 



(FS) 



f; ^ = 



(FS)- r (FS) 



F5 = -J dxxB(x) p^^^ (x,t) 



( FS) 



150 



